Direct computing of entropy from time series

Abstract

Measure Theoretic Entropy and its important properties are studied. We introduce a method to compute entropy of a dynamical system directly from the definition. The computational approach is discussed in detail and is presented in several sections: (1) Partitioning and Scaling Data; (2) Sequencing and Compactification; (3) Probabilities and Information; (4) Entropy Estimation. Also, we apply the same method in two dimensions. A model for filtering entropy based on skew products is given, and we apply our computational results to verify this model.